T. Schoen

activity

20072023

most citedAdditive dimension and a theorem of Sanders

13 citations · 26 across the 12 of their papers we have counts for

collaborators

16 papers

math.CO2023

New bounds in the Bogolyubov-Ruzsa lemma

Tomasz Kosciuszko, Tomasz Schoen

We establish new bounds in the Bogolyubov-Ruzsa lemma, demonstrating that if A is a subset of a finite abelian group with density alpha, then 3A-3A contains a Bohr set of rank O(lo…

math.CO2023

On convex equations

Tomasz Schoen

We prove that every subset of ${1, \dots, N}$ which does not contain any solutions to the equation $x + y + z = 3 w$ has at most $exp (- c (lo g N)^{1/5 + o (1)}) N$ elements, for some $c > 0$ .…

math.CO2023

Note on the Theorem of Balog, Szemerédi, and Gowers

Christian Reiher, Tomasz Schoen

We prove that every additive set $A$ with energy $E (A) \geq ∣ A ∣^{3} / K$ has a subset $A^{'} \subseteq A$ of size $∣ A^{'} ∣ \geq (1 - ε) K^{- 1/2} ∣ A ∣$ such that $|A'-A'|\le O_\varepsilon(K^{…

math.CO2020

A subexponential upper bound for van der Waerden numbers W(3,k)

Tomasz Schoen

We show an improved upper estimate for van der Waerden number $W (3, k) :$ there is an absolute constant $c > 0$ such that if ${1, \dots, N} = X \cup Y$ is a partition such that $X$ does n…

math.NT2020

Improved bound in Roth's theorem on arithmetic progressions

Tomasz Schoen

We prove that if $A \subseteq {1, \dots, N}$ does not contain any non-trivial three-term arithmetic progression, then $∣ A ∣ ≪ \frac{( lo g lo g N ) ^{3 + o (1)}}{lo g N} N .$

math.NT2020★ 1 cited

Character sums estimates and an application to a problem of Balog

Tomasz Schoen, Ilya D. Shkredov

We prove new bounds for sums of multiplicative characters over sums of set with small doubling and applying this result we break the square--root barrier in a problem of Balog conc…